# Are metals more heavy due to the Earth's magnetic field?

Non-metal objects are attracted to the Earth due to gravity. So the weight of non-metal objects can be only dependent on their mass.

On the other hand metals can be attracted to the Earth's magnetic field, with the Earth acting as a giant magnet; causing metals to weight more than they normally should.

In other words the weight of metals and magnetic objects would be the sum of the magnetic force plus the gravitational force, is that correct?

If that effect is true, would it be more clear as we go closer to the magnetic poles, and metals would weigh different in different locations on Earth?

• I guess that you would have to consider the direction of the force. But you can be sure that the effect will be negligible, zero most experiments. You could also consider other electromagnetic forces, like Van der Waals attraction. – jinawee Feb 21 '14 at 16:03
• if you go closer to the magnetic poles ($\approx$ geographical poles) even a non magnetic object will weight more as you are closer to the Earth centre and there is less centrifugal force there. I suspect that both these effects are quite bigger than the magnetic attraction. – DarioP Jul 21 '14 at 11:04

Reformulating your question: do metals feel a force of attraction to the earth due to the earth's magnetic field - and does that force depend on the position on earth?

It is not the magnetic field itself that causes the attraction, it is the gradient of the magnetic field. In a uniform magnetic field you will get some magnetization (more so in ferromagnetic materials), and there will in general be a torque as the dipole moment in the material tries to align with the external magnetic field. This is the principle behind a magnetic compass, but in itself does not result in a net force (of the kind that you could measure on scales).

In a non-uniform field,

$$F = (\mu \cdot \nabla) B$$

Now with the magnetic field of a dipole scaling roughly with $\frac{1}{r^3}$, we know that the gradient will be approximately $3B/r$. Since $r$ is the radius of the earth, dividing $B$ by a large number makes a very, very small number. And because you are taking the dot product, with the magnetization being aligned with the magnetic field and the gradient being at right angles (at the equator), it will be zero. But as you approach the poles, the magnetization and the gradient will start to align somewhat.

So yes - there will be a force on ferromagnetic objects due to the earth's magnetic field, and that force changes with position on earth - greatest near the magnetic poles, smallest near the equator. But it will be absolutely tiny, and you will have a very hard time measuring it.

Floris's answer gives you an excellent description of the forces that would be present in both a magnetic and gravitational field, whilst MaxGraves's Answer gives you a clear and careful discussion of how you should use the word weight.

In more the spirit of MaxGraves's Answer, something that seems a little pedantic but may be interesting to you is the following: by dint of the magnetic field's having been set up within the body, the body "contains" an energy of genesis of the magnetic field $\frac{1}{2}\,\,B_\oplus^2\,V/\mu$ (the energy needed to set up the field within the body), where $B_\oplus$ is the Earth's magnetic induction and $\mu$ the material's magnetic constant. For ferromagnetic cores, this will be of the order of $1000\,\mu_0$ or more. $V$ is the body's volume.

So the body - to a minute degree - actually feels a higher gravitational force owing to its now minutely higher energy content. The extra gravitational (= inertial) mass it gains owing to this exquisitely small effect is $E/c^2\approx\frac{1}{2}\,B_\oplus^2\,V/(c^2\,\mu)$. For a body with $\mu=1000\,\mu_0$, a volume of $10^{-3}{\rm m^3}$ (a litre) and, taking $H_\oplus$ to be $50\mu T / \mu_0$ we get a mass increase of

$$(5\times10^{-5})^2\times 10^{-3} /(2000\times4\pi\times10^{-7}\times 9\times 10^{16}){\rm kg}\approx10^{-26}{\rm kg}$$

i.e. about the mass of ten protons, or one boron nucleus!

I believe that the commonly accepted definition of weight is

''the force of gravitational attraction that the earth exerts on your body''

University Physics, Young and Freedman, 11th edition, page 120

So I would say no, the weight cannot be affected by any electromagnetic fields, by the true definition of weight.

If by weight you mean the number read off of a standard scale, then sure. Imagine placing a magnet under the table that a scale is sitting on and then massing an magnetic object. It would read differently than without the magnet. The earth's magnetic field is very weak compared to most magnets you are used to dealing with though so I would wager the difference would be negligible and probably not detectable by most instruments if only considering the magnetic field from the earth.

• "The earth's magnetic field is very weak compared to most magnets" How weak are we talking about? Isn't that magnetic field responsible for deflecting solar winds which are considered formidable? – Ray Feb 21 '14 at 16:39
• @Ray Look here for some numbers: en.wikipedia.org/wiki/Gauss_%28unit%29 For a small magnet, say 200x more. BUT, Earth's magnetic field spans across very large distances. Bit a bit, the particles are effectively deflected across a long path. – Davidmh May 26 '14 at 12:02

Many common metals are diamagnetic, $\chi_{\text{molar}}$, $10^{-6}$cm$^3$mol$^{-1}$: Cu -5.46, Zn -9.15, Ga -21.6, Cd -19.7, In -10.2, As(grey) -5.6, Ag -19.5, Te -38, Sn(grey) -37.4, Au -28, Hg -33.5, Tl -50, Pb -23, Bi -280.1 They are repelled from a magnetic field.

Either way, the effect is overall small in a mildly divergent 0.4 gauss field. Obvious exceptions are ferromagnets and the strongest paramagnets. The strongest diamagnets/gram are graphite parallel to its graphene plane and bismuth.

You seem to be a victim of the common confusion between the terms weight, gravity and gravitation.

First the similarities. They involve forces and acceleration.

The differences.

• Weight is the SUM of all downward and upward FORCES irrespective of their origins and points of action. Weight is essentially the supportive or opposing force required to keep something from moving (actually accelerating) upwards or downwards relative to a planetary body.
• Gravity is the sum of all downward and upward ACCELERATIONS towards or away from a planetary body. You may have heard of zero-gravity or negative g's. These are not really the absence or reversal of gravity; they are merely a set of upward forces that cancel out or exceed the usual downward forces.

Weight is simply mass x gravity WF = m.g

• Gravitation is a unique force that occurs between all matter. Gravitation has no upwardness or downwardness. Gravitational is simply a SINGLE force that exists between two objects by virtue of their mass and distance. Gravitation IS NOT a sum of forces; it is one of the forces or force mechanisms that exist alongside mechanical, electric and magnetic forces.

When a large planetary body such as the earth is involved, the major component of weight and gravity is due to the planet's gravitation; the other components may be

• upthrust- forces due to immersion in a fluid (liquid or gas),
• mechanical support,
• aerodynamic or hydrodynamic forces (drag and lift due to moving air or moving liquids),
• magnetic and electric forces due to magnetic rocks in the ground and electrical forces in the air, space, ground or roof,
• vertical centripetal forces such as those in hill climbing vehicles, aircraft, swings etc.

The main aspect of interest in weight and gravity is the vertical nature of the net force. Obviously, the term vertical is relative and that is why weight and gravity are only defined in relation to a large free body such as a planet.

Essentially, weight depends on where you are, what you are, what you are carrying and how you are moving. Weight and gravity are slightly less at the equator than at the poles because of the earth's bulge and the higher centripetal force (due to the earth's spinning).

Weight changes slightly (and negligibly) as the Moon or Sun passes overhead or underfoot and this is the cause of tides. High tides occur at roughly the time when the gravitational action of the Sun or Moon causes the weight of the ocean water to reduce.

A measurement of atmospheric pressure is essentially a measurement of the weight of the air above the barometer. Since air pressure changes, then the weight exerted on you by the air also changes (negligibly, except at high altitudes or in deep sea diving).

The gravitational pull of a trailer acting on an insect cannot be termed as either weight or gravity but it does contribute to the weight of the insect relative to the earth. Part of your weight on earth is due to the Sun pulling you upwards when overhead or downwards at midnight). The electric field of your own body is strong enough to counter the weight of dust particles and that is why they stick to your skin.

Strong winds and flood waters lift objects by causing a reduction in weight (not gravitation) through addition of upward force components. The presence of magnetic and electric rocks can and does cause noticeable changes in weight. In some places, this causes objects to roll uphill geographically although they are actually rolling downhill in terms of gravity, weight and potential energy. It is much like a steel nail been attracted uphill by a magnet.

The presence of the magnetic poles at the geographical poles may cause a slight variation in weight but the effect would be two weak to verify. Substances such as water would be repelled and weigh less while magnetic objects would way more. Magnets would weigh more or less depending on the poles that faces down towards the earth's poles. These changes in weight are probably to weak to be measured outside the margins of error due to other influences.

the trm "weight" in its own mean the net mass of the metal + the gravitational force. we see that the non-metals are not attracted towards magnets. earth, being a giant magnet, attracts metals only. thus, the weight of the non metals is mass + gravitational force on the other hand, metals have higher masses too. so their weight is mass + gravitational force + the force of earth acting as a magnet.

• That's not at all what "weight" is. Gravitational force depends on mass. – HDE 226868 Aug 20 '14 at 17:46